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Related Concept Videos

Adsorption Isotherms II01:25

Adsorption Isotherms II

Brunauer, Emmett, and Teller (BET) introduced a theory in 1938 that modified Langmuir's assumptions to explain multilayer physical adsorption. This theory is applicable to Type II isotherms and provides a more realistic picture of adsorption processes. The BET theory assumes a uniform solid surface with localized adsorption sites, where adsorption at one site doesn't affect adsorption at neighboring sites. This theory also allows for the possibility of additional molecules being adsorbed on top...
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Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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The Entropy as a State Function01:14

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Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
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Related Experiment Video

Updated: May 13, 2026

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
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Information theoretic aspects of the two-dimensional Ising model.

Hon Wai Lau1, Peter Grassberger

  • 1Complexity Science Group, University of Calgary, Calgary, Canada T2N 1N4.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 19, 2013
PubMed
Summary

We studied information theoretic properties of the Ising model. The excess entropy of a cylinder and a line of spins diverge logarithmically at critical points, suggesting a universal behavior in phase transitions.

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Area of Science:

  • Statistical Mechanics
  • Information Theory
  • Condensed Matter Physics

Background:

  • The Ising model is a fundamental tool for understanding phase transitions.
  • Information theoretic properties offer new insights into critical phenomena.

Purpose of the Study:

  • To numerically investigate information theoretic properties of the square lattice Ising model.
  • To quantify finite length corrections to entropy and analyze excess entropy.
  • To explore the behavior of mutual information and excess entropy at critical points.

Main Methods:

  • Bond propagation algorithm for entropy calculations.
  • Transfer matrix method for precise estimations.
  • Monte Carlo simulations for excess entropy analysis.

Main Results:

  • Quantified finite length corrections to entropy scaling with cylinder circumference.
  • Calculated mutual information between cylinder halves, confirming previous results with higher precision.
  • Observed logarithmic divergence of mutual information and excess entropy at the critical point.
  • Conjectured generic logarithmic divergence for 1D subsets at 2D second-order phase transitions.

Conclusions:

  • The study provides precise numerical results for information theoretic properties of the Ising model.
  • Logarithmic divergences in mutual information and excess entropy are observed at criticality.
  • The findings suggest universal behavior for one-dimensional subsets at second-order phase transitions.